Quantitative comparison of Taylor flow simulations based on sharp-interface and diffuse-interface models

2013 ◽  
Vol 73 (4) ◽  
pp. 344-361 ◽  
Author(s):  
S. Aland ◽  
S. Boden ◽  
A. Hahn ◽  
F. Klingbeil ◽  
M. Weismann ◽  
...  
Keyword(s):  
Quantitative Comparison ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Flow Simulations ◽  
Taylor Flow ◽  
Interface Models

scholarly journals THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

2012 ◽  
Vol 22 (03) ◽  
pp. 1150013 ◽  
Author(s):  
HELMUT ABELS ◽  
HARALD GARCKE ◽  
GÜNTHER GRÜN
Keyword(s):  
Surface Diffusion ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Momentum Balance ◽  
Two Phase ◽  
Interface Models ◽  
Natural Energy ◽  
Soluble Species ◽  
Sharp Interface Models ◽  
Dissipation Inequalities

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is frame indifferent. Moreover, it is generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation, we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the latter case a new term resulting from surface diffusion appears in the momentum balance at the interface. Finally, we show that all sharp interface models fulfill natural energy inequalities.

scholarly journals On sharp interface limits for diffuse interface models for two-phase flows

2014 ◽  
Vol 16 (3) ◽  
pp. 395-418 ◽  
Author(s):  
Helmut Abels ◽  
Daniel Lengeler
Keyword(s):  
Sharp Interface ◽  
Diffuse Interface ◽  
Two Phase Flows ◽  
Two Phase ◽  
Interface Models

Sharp-interface limit of the Cahn–Hilliard model for moving contact lines

2010 ◽  
Vol 645 ◽  
pp. 279-294 ◽  
Author(s):  
PENGTAO YUE ◽  
CHUNFENG ZHOU ◽  
JAMES J. FENG
Keyword(s):  
Contact Line ◽  
Diffusion Length ◽  
Slip Length ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Contact Lines ◽  
Sharp Interface Limit ◽  
Interface Models ◽  
Moving Contact ◽  
Moving Contact Lines

Diffuse-interface models may be used to compute moving contact lines because the Cahn–Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the basic questions underlying this approach. Through scaling arguments and numerical computations, we demonstrate that the Cahn–Hilliard model approaches a sharp-interface limit when the interfacial thickness is reduced below a threshold while other parameters are fixed. In this limit, the contact line has a diffusion length that is related to the slip length in sharp-interface models. Based on the numerical results, we propose a criterion for attaining the sharp-interface limit in computing moving contact lines.

scholarly journals Wetting failure and contact line dynamics in a Couette flow

2008 ◽  
Vol 614 ◽  
pp. 471-493 ◽  
Author(s):  
M. SBRAGAGLIA ◽  
K. SUGIYAMA ◽  
L. BIFERALE
Keyword(s):  
Capillary Number ◽  
Slip Length ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Control Parameters ◽  
Interface Models ◽  
Critical Capillary Number ◽  
Stationary Interface ◽  
Interface Treatment

Liquid–liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters – capillary number, viscosity ratio and separation of scale – i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau–Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.

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